The last decades have witnessed a thriving investigation into understanding fundamental light-matter interactions and a rapid advance in atomic, molecular, and optical experimental techniques. Nonlinear phenomena enabled by intense light sources in the optical, infrared, and microwave regions have been utilized to control electronic, nuclear, and spin degrees of freedom which have led to breakthroughs across many fields of science, such as medical imaging, telecommunication, and the creation and manipulation of novel materials. The advent of X-ray free-electron lasers (XFELs) offers unprecedented high-brightness x-ray pulses, thus opening the pathway to nonlinear light-matter interactions in the x-ray regime. The successful observation of several nonlinear x-ray optical phenomena and ultrafast pump/probe experiments using XFELs have suggested that transferring nonlinear optical spectroscopy to x-ray regimes is a feasible and fruitful approach. Among these emerging tools, one essential building block of nonlinear x-ray spectroscopy is stimulated x-ray Raman scattering (SXRS), which can simultaneously achieve a sub-femtosecond temporal and sub-core-hole lifetime energy resolution. SXRS is proposed to probe the ultrafast charge transfer in complex systems such as proteins on its natural attosecond time scale with atomic resolution. In this PhD thesis, I studied resonant propagation of strong XFEL pulses through a dense medium both theoretically and experimentally. The coupled time-dependent Schrodinger equation (TDSE) and Maxwell wave equation (MWE) are solved to simulate this process, and an experiment at European XFEL was performed. The TDSE-MWE simulations revealed interesting x-ray nonlinear phenomena such as SXRS, x-ray lasing, self-induced transparency, and self-focusing. The experiment takes advantage of the stochastic x-ray pulse structure and covariance analysis is used to obtain an unprecedented high-energy-resolution SXRS spectrum. With the simulations on the supercomputer, we obtained new insights into SXRS as well as ways to improve it. The inclusion of the incident x-ray spectrum information would benefit SXRS, and a ghost-imaging method is demonstrated to characterize the incident x-ray spectrum with high resolution non-invasively. In general, this PhD research contributes to the development of nonlinear x-ray spectroscopy with XFELs.